Describe compression and rarefaction

3.4 Sound – Compression and Rarefaction

1. What is a Longitudinal Wave?

A longitudinal wave is one in which the particles of the medium vibrate parallel to the direction of wave travel. Sound, seismic P‑waves and pressure waves in fluids are all longitudinal.

2. Production of Sound by a Vibrating Source

When a solid object (e.g., a tuning‑fork, a speaker diaphragm or a guitar string) vibrates it repeatedly displaces the adjacent air particles:

• Forward stroke – the source pushes the nearby particles together, creating a region of higher pressure – a compression.
• Backward stroke – the source pulls the particles apart, producing a region of lower pressure – a rarefaction.

This alternating push‑pull motion generates a series of compressions and rarefactions that travel away from the source at the speed of sound.

3. Need for a Material Medium

Sound requires a material medium (gas, liquid or solid) because the wave is a succession of particle interactions. In a vacuum there are no particles to transmit the pressure changes, so sound cannot travel.

4. Audible Frequency Range

Human ears can detect sound frequencies from 20 Hz to 20 kHz. Within this range the pitch we perceive is directly related to the frequency of the compressions‑rarefactions reaching the eardrum.

5. Compression and Rarefaction

• Compression – a region where particles are pushed together, giving a local increase in pressure and density.
• Rarefaction – a region where particles are spread apart, giving a local decrease in pressure and density.

Key Characteristics

6. How Compression and Rarefaction Form a Sound Wave

1. Compression – particles are crowded together.
2. Rarefaction – particles are drawn apart.
3. The pattern repeats, travelling through the medium at the speed of sound.

7. Relationship to Wave Parameters

The distance between two successive compressions (or two successive rarefactions) is the wavelength \( \lambda \). The number of compressions that pass a fixed point each second is the frequency \( f \). The speed of sound \( v \) links these quantities:

$$ v = f\lambda $$

During a compression the instantaneous pressure \( p \) exceeds the equilibrium pressure \( p_0 \); during a rarefaction it falls below \( p_0 \).

8. Speed of Sound in Different Media

The Cambridge syllabus states that the speed of sound in air is **330 – 350 m s⁻¹**; the value 340 m s⁻¹ given above lies comfortably within that range.

In general, sound travels faster in media that are more rigid (higher bulk modulus) and less compressible.

9. Everyday Examples

• Speaking – vocal‑cord vibrations create rapid compressions and rarefactions that travel to the listener’s ear.
• Musical instruments – a plucked guitar string, a struck drumhead or a blowing reed all set the surrounding air into alternating high‑ and low‑pressure regions.
• Ultrasound imaging – high‑frequency sound waves (> 20 kHz) produce very short‑wavelength compressions/rarefactions that reflect from body tissues, allowing internal structures to be visualised.
• Sonar – ships emit sound pulses; the returning compressions and rarefactions reveal the position of underwater objects.

10. Suggested Diagrams (for classroom use)

11. Summary

1. Sound is a longitudinal wave consisting of alternating compressions (high pressure, high density) and rarefactions (low pressure, low density).
2. A vibrating source creates these regions by pushing and pulling the surrounding particles.
3. The compression‑rarefaction pattern travels through any material medium at a speed that depends on the medium’s properties (≈ 340 m s⁻¹ in air, 1 500 m s⁻¹ in water, 5 000 m s⁻¹ in steel).
4. Human hearing covers 20 Hz – 20 kHz; within this range frequency determines pitch, while amplitude determines loudness.
5. Understanding compressions and rarefactions explains how sound is produced, transmitted and received in everyday life and in technologies such as ultrasound and sonar.